Elsevier

Computer Networks

Volume 50, Issue 18, 21 December 2006, Pages 3721-3742
Computer Networks

Predictive buffer control in delivering remotely stored video using proxy servers

https://doi.org/10.1016/j.comnet.2006.04.004Get rights and content

Abstract

We study the problem of using proxy servers to stream video stored at a geographically separate location. The separation of the server and the storage introduces a non-negligible delay in retrieving video frames in real time. We assume an additive-increase/multiplicative-decrease transport protocol to support the streaming process and develop an effective scheme to achieve consistent, high streaming quality. The heart of the scheme is the control of buffer occupancy at the proxy server. We model the buffer as a bilinear dynamical system disturbed by a point process with stochastic state-dependent intensity. We first develop a buffer controller that does not exploit this model. Then, using the buffer model, we construct a second controller based on an optimal-control analysis for the case without retrieval delay. Extending these two controllers, we subsequently synthesize two controllers based on prediction of future system states using the model, taking into account both the delay and the state-dependent disturbance intensity. Our empirical study illustrates the effectiveness of the streaming scheme. We further find that the controllers exploiting the buffer model demonstrate performance significantly superior to that of the model-free controller in overcoming the adverse impact of the retrieval delay. We also conduct limited experiments to study the impact of variable retrieval delays.

Introduction

We study the problem of a proxy server streaming video, stored at a distant location, to clients and develop an effective scheme to achieve consistent, high visual quality of the streamed video. A proxy server can be placed at the edge of wide-area networks (WANs) and close to clients to participate in online video delivery for several purposes. Fig. 1 illustrates an example scenario. First, when necessary, the proxy server can decompress and re-compress the video frames received from the central storage to fit the varying bandwidth of the connection from the proxy server to the clients (this procedure is called transcoding). In such a configuration, the central storage is relieved from the burden of transcoding which is computationally expensive. A second purpose is for enhanced network security, because now the only access point to the local-area network (LAN) is the proxy server, which can be fortified against possible malicious attack. Third, the proxy server can help keep the bandwidth manageable required from WANs [1]. The idea is to choose a cutoff size for video frames stored at the central storage and break each frame into two parts: one is of the cutoff size, the other the frame size reduced by the cutoff size. The latter partial frames are pre-fetched by and stored at the proxy server. When a streaming request arrives, the proxy server, in real time, retrieves partial frames stored at the central storage, assembles them with local partial frames, transcodes the restored complete frames, and finally transmits the transcoded frames to the client via the LAN. Since partial frames fetched from the central storage are no larger than the cutoff size, the usage of the expensive WAN bandwidth is limited. Making use of the limited storage space at the proxy server this way, the savings in the WAN bandwidth can be substantial. See [32], [33] for more work on proxy-assisted multimedia streaming.

We wish to develop a streaming scheme executed at the proxy server to achieve consistent visual quality (within a scene in the video) and high visual quality in streaming for the aforementioned scenarios. (We note that conventional streaming scenarios that involve only locally stored video is a special case of the broader situation we consider here.) By “quality consistency”, we mean smooth changes in the quality of adjacent video frames within a scene. Abrupt changes will cause an artifact of “flickering (or blinking)” display of the video, annoying to viewers [2]. Toward this end, we aim to reduce the variance in encoding bit-rates in the transcoding process within a scene; encoding bit-rates determine frame sizes, which are intimately related to visual quality through rate-distortion functions [24]. Consistent quality can obviously be achieved by setting encoding bit-rates according to related rate-distortion functions. However, in our solution, we simply set the encoding bit-rate to a constant for frames of the same type to ensure roughly consistent visual quality within a scene; we do not address the problem of attaining consistent quality between scenes, which is significantly more involved and demands separate work. This simple feature of our scheme also facilitates the solution of the buffer-management problem described later. High visual quality is also reflected in the throughput and the packet loss rate that the streaming application attains. The larger the throughput and/or the smaller the loss rate, the better the overall quality. We desire to use the bandwidth offered by the underlying transport protocol to the maximum extent possible, to achieve high throughput, while at the same time maintain a low packet loss rate. Our approach to accomplish high throughput and low loss rates is through intelligent buffer control exercised at the proxy server.

Two features distinguish our streaming problem from previous research. One is the presence of a retrieval delay arising from the physical distance between the proxy and the central storage servers. In the streaming process, it takes the proxy server a non-negligible amount of time to retrieve a particular frame from the central storage. This delay greatly complicates the buffer-control problem. We also call this retrieval delay the control delay of the system.

The other feature of our problem is that we assume an additive-increase/multiplicative-decrease (AIMD) transport protocol supports the streaming application and that we explicitly exploit the characteristics of such a protocol for quality streaming. Roughly speaking, an AIMD protocol linearly increases its transmission rate to probe for more network bandwidth available to use when there is no congestion and immediately reduces the rate by a factor (usually constant) when congestion is detected. The success of the Internet over the past decade suggests that AIMD behavior is crucial for network stability. In fact, the Transmission Control Protocol (TCP), dominant in the Internet, is a typical AIMD protocol. The down side is that AIMD protocols suffer from jittery transmission rates; see Fig. 2. Fig. 2 is obtained using the Rate Adaptation Protocol (RAP), a well-known AIMD protocol suitable for real-time media delivery [4]. The rate variation in Fig. 2 is due both to bursty interfering traffic and to the AIMD behavior of RAP (which reduces the rate by a half when encountering congestion).

The equation-based transport protocols [5] can achieve smoother transmission rates than those of AIMD protocols. However, we demonstrate in Fig. 3 that in real network scenarios the result is still far from satisfactory. We obtained the shown result using a typical equation-based protocol called the TCP-Friendly Rate-Control (TFRC) Protocol [6]. When bursty interfering traffic is present, TFRC is unable to remove jitter at large timescales (e.g., seconds) and may produce flickering artifacts within a scene (which usually lasts for seconds or minutes) if used in video streaming.

We assume an underlying rate-based AIMD transport protocol based on the following reasons. First, it stabilizes the network, critical for healthy network operation. Second, its behavior allows tractable mathematical characterization and thus enables a control-theoretic analysis of the problem. Finally, AIMD transport protocol can easily be tuned to be TCP-friendly; i.e., it shares network bandwidth with TCP connections in a fair way [4], a highly desirable property. We rule out equation-based protocols because they do not produce satisfactorily smooth rates, they have uncertain impact on network stability, and they are not widely deployed in practice.

Two difficulties arise in controlling the buffer occupancy at the proxy server: the control delay and the stochastic wide-band variation of the transmission rate of the underlying AIMD protocol. Without proper control, the buffer can easily underflow/overflow, resulting in throughput loss. With AIMD protocols, underflow loss can be significant because, when the buffer is empty, not only is no data transmitted but also the drain rate stops increasing, leading to lower drain rate in the future. The buffer can easily overflow, too, resulting in excessive loss of packets. One might think that a large buffer solves the problem. For instance, to roughly ensure consistent visual quality for the same type of frames within the same scene, one can transcode all video frames according to the actual average transmission rate of the AIMD protocol (transmission rate, for short) and injects transcoded frames into the buffer, hoping that the large buffer will absorb the variations in the transmission rates and thus that high visual quality can be achieved. However, our experiment with RAP shows that to have an acceptable packet loss rate of 10−3 (see [7]), this scheme requires a buffer 10 times as large as that required by the best controller among the ones we develop in this paper. Such dimensioned buffer increases the memory cost significantly and causes unwanted large average delay and large delay jitter, because the queue size inevitably oscillates between the full and the empty buffers. (We use buffer and queue interchangeably in the paper.) Although memory is inexpensive these days, its cost still constitutes a good portion of a computer system. It is apparent that using a large buffer this way is not a good solution. Therefore, we wish to develop controllers that achieve high quality using a relatively small buffer. We prioritize consistent quality (within a scene) over high quality because we believe a jittery display of the video results in more dissatisfaction than video presented with constant quality, even if the average throughput of the latter is smaller.

We develop four solution methods for the buffer-control problem in this paper. We first provide a straightforward controller that does not assume any system model. We then formulate the buffer-control problem as a stochastic bilinear quadratic optimal tracking problem with a control delay. The stochastic system disturbance is bilinear in terms of the system state and of a point process with state-dependent stochastic intensity. In our earlier work [3], we modeled the disturbance as a Poisson process, common in modeling congestion in TCP networks [8], [11], [14]. In contrast, our formulation here includes the dependence of the intensity of the disturbing point process on the system state. This more realistic and more sophisticated model is of interest in its own right; it can be closely related to a well-known TCP model (see detailed discussion on this in a later section). This model enables us to derive two new controllers that achieve much improved performance over the controllers in [3]. In [9], the author studies the optimal regulator problem of linear systems disturbed by Poisson processes for the control-delay-free case; however, no complete solution is given. The authors of [10] study control of manufacturing systems with Poisson disturbance and without control delay, and propose dynamic-programming methods as solutions. In [8], [11], [14], the authors model a TCP connection as a system with a Poisson disturbance to facilitate fluid simulation or a queueing analysis of TCP networks. Like in this paper, the disturbance term in the system dynamics in [8], [9], [10], [14] is bilinear in the system state and in the disturbing Poisson process; however, the intensity of the Poisson process itself there is independent of the system state. The authors in [11], [12] implicitly uses a state-dependent intensity. In contrast, our problem involves both a control delay and a (more general) disturbance point process with stochastic state-dependent intensity.

The contribution of this paper lies in the fact that we are the first to address the problem of buffer control for video-streaming involving geographically separated proxy servers and video content, developing an effective scheme for quality video streaming. A second contribution is that three of the developed buffer controllers are specifically designed for bilinear dynamical systems with Poisson disturbance or, more generally, with point-process disturbance with state-dependent intensity. Furthermore, our system has a control delay. To our knowledge, our work here is the first towards effectively controlling such systems. A third contribution is that through our comparative study on model-free and model-based controllers, we demonstrate that using a proper model, a controller can outperform a model-free controller by a significant margin.

This report is structured as follows. In Section 2, we formally describe the problem and present our general approach, with the emphasis on formulating the buffer control as an optimization problem. Section 3 contains our main results in solving the buffer-control problem. We first present a model-free controller as a straightforward heuristic solution, which serves as a comparison basis for the three model-based controllers we construct subsequently. The first model-based controller is in fact the optimal solution to the case where the control delay is absent and the intensity of the disturbing point process is constant (making the point process Poisson in this case). We henceforth call this controller the zero-delay optimal controller. We then develop two controllers that heuristically take into account the control delay and the state-dependence of the point-process disturbance, by predicting future system states using the buffer model. One of these two prediction-based controllers is built upon the model-free controller, while the other is a natural extension of the zero-delay optimal controller. We provide in Section 4 our empirical results demonstrating the effectiveness of our solution scheme. Section 6 concludes the paper.

Section snippets

System model

Fig. 4 shows a block diagram of the system shown in Fig. 1. The controller, the transcoder, the AIMD transport protocol, and the buffer are the essential components within the proxy server, and their detailed descriptions are given below. We have the following assumptions. Time t is continuous. The frame rate of the video is F frames per second. Only the first frame of the transcoded video is intra-coded while all the rest are inter-coded into the same type (e.g., P type), as in [13]. The

A model-free controller

We first present a straightforward heuristic solution to optimizing (12). This controller does not make decisions with any regard to the cost function in (12). In fact, the controller does not exploit any model of the buffer dynamics and is unaware of the retrieval delay. We construct this controller for two purposes: to have a simple solution to the buffer-control problem, and to use it as a comparison basis for the three controllers we will develop next, which explicitly exploit the buffer

Evaluation setup

Our empirical study is carried out on a simulated network shown in Fig. 5 using the network simulator ns version 2. As shown, four source-destination pairs, numbered (Si, Di), i = 1,  , 4, share the same link between the routers R1 and R2. Traversing from S1 to D1 is a real traffic trace captured by the National Laboratory for Applied Network Research (http://www.nlanr.net), representing bursty traffic often seen in real networks and simulating interfering traffic not responding to congestion. Two

Discussions and future directions

The video-streaming scheme presented in this paper employs a point-process model and a control-theoretic approach and also uses a series of heuristics and simplifying assumptions. Many of the heuristics and assumptions can be discussed and can be possibly further improved. Along these lines, in this section we discuss some aspects of the problem formulation and the solutions.

Although the performance of our schemes is promising, one important problem suggests further study. We intra-code only

Conclusions

We study a problem of streaming stored video that includes geographically separated proxy servers and video data, and develop a scheme effectively achieving consistently high streaming quality (within a scene). Underlying the scheme is a controller that intelligently manages the buffer occupancy to attain high utilization while maintaining low packet loss rates. We propose a general point process as a model of the loss process within the delivery network. We offer four choices of the buffer

Acknowledgements

The authors sincerely acknowledge the useful comments from anonymous reviewers, especially on the points regarding time-scale and stability issues presented in the Discussion and Future Directions section.

Gang Wu received his Ph.D. degree in Electrical and Computer Engineering from Purdue University in 2003. At Purdue, he carried out research on decision-making and analysis in stochastic communications networks, exploring optimization and analytical techniques involving Markov decision processes, self-exciting point processes, and reflected Brownian motion. He joined Fair Isaac Corporation in 2003 and is now an Analytic Science Manager, leading a group of scientists in building statistical

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  • Cited by (3)

    Gang Wu received his Ph.D. degree in Electrical and Computer Engineering from Purdue University in 2003. At Purdue, he carried out research on decision-making and analysis in stochastic communications networks, exploring optimization and analytical techniques involving Markov decision processes, self-exciting point processes, and reflected Brownian motion. He joined Fair Isaac Corporation in 2003 and is now an Analytic Science Manager, leading a group of scientists in building statistical models to detect network-threatening events, to discover revenue-leakage points in billing processes, to manage credit risk, and to detect fraudulent activities, all in communications networks.

    Edwin K.P. Chong received the B.E.(Hons.) degree with First Class Honors from the University of Adelaide, South Australia, and the M.A. and Ph.D. degrees from Princeton University, where he held an IBM Fellowship. He joined the School of Electrical and Computer Engineering at Purdue University in 1991, where he was named a University Faculty Scholar in 1999, and was promoted to Professor in 2001. Since August 2001, he has been a Professor of Electrical and Computer Engineering and a Professor of Mathematics at Colorado State University. His current interests are in communication networks and optimization methods. He coauthored the recent best-selling book, An Introduction to Optimization, 2nd ed., Wiley-Interscience, 2001. He was on the editorial board of the IEEE Transactions on Automatic Control, and is currently an editor for Computer Networks. He is a Fellow of the IEEE, and served as an IEEE Control Systems Society Distinguished Lecturer. He received the NSF CAREER Award in 1995 and the ASEE Frederick Emmons Terman Award in 1998. He was a co-recipient of the 2004 Best Paper Award for a paper in the journal Computer Networks.

    Robert Givan is an Associate Professor in the School of Electrical and Computer Engineering at Purdue University. He received his B.S. degree in Mathematics and Biology from Stanford University in 1987 and his Doctorate in Computer Science from the Massachusetts Institute of Technology in 1996, where he held the Fannie and John Hertz graduate fellowship. He joined Purdue in the fall of 1997 after one year of postdoctoral research at Brown University. His research is on the foundations of artificial intelligence, including machine reasoning, learning, and planning. He has also worked on applications of related algorithms to the pricing and control of computer networks as well as branch prediction in computer architecture. He was the recipient of an NSF CAREER Award in 2001.

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